The angle subtended at the centre of the great or small circle by the minor arc joining two places on the great or small circle respectively, is called the angular difference between the two places. We shall consider the following:

- differences in angles of longitude
- differences in angles of latitude.

#### Differences in the angles of longitude

When the two points are located on the same side on the earth’s surface i.e. Either East-East or West –West, subtract the angles, otherwise, add them up.

Examples

- Abuja is located on 32o E while Lagos is on 15oE. What is the difference in their angles of longitude? (both lie on Lat. 60oN).
- Calabar is on 15oE of the meridian , while Lokoja is located on 120N, find the difference in their angles of longitude (both on latitude 40o S)

Solution

Difference in angle = 32o – 15o = 17o

Angular difference = 12 + 15 = 27o

#### Evaluation

- Ogun is located on 100W and Uyo on 50o W. Both lies on latitude 40oN. What is the angular difference?
- Find the angular difference between the following pairs of places on the Earth’s surface.
- Ketu ( 32oS, 20oE) and Lekki ( 32oS, 65oE)

- Gombe (20oN, 10oW) and Abuja (20oN, 45oE)

#### Differences in the angles of latitude

When two points are located on the same side along the same longitude on the earth’s surface i.e North-North, South-South, subtract the angles otherwise add them up.

Example: Find the angular difference between the following pairs of places on the Earth’s surface.

- Paris (35oN, 40oE) and Rome ( 25oS, 40oE)
- Oyo ( 80oS, 27oW) and Edo (47o S, 27oW).

Solution

Angular difference = 25 + 35 = 60o

Angular difference = 80 -47 = 33o

#### Evaluation

Find the angular difference between the following pairs of places on the Earth’s surface.

- P (30oS, 48oE) and Q ( 60oS, 48oE)
- R ( 22oS, 60oW) and S (38oN and 60oW)

#### DISTANCES ALONG THE GREAT CIRCLES

The great circles are only lines of longitude and equator which is 0o. Therefore distances along the lines of longitude will majorly be the focus. Their radii are the same as the radius of the earth ( R). The knowledge of mensuration shall be used to calculate the distance along the lines of longitude.

#### Distance along the great circle = Өo x 2πR (where R is the radius of the earth) 3600

#### Evaluation

1.A plane flies due East from A (lat. 530N, long 250E) to a point B (lat 530N, long. 850E) at an average speed of 400km/hr. the plane then flies due south from B to a point C, 2000km away. Calculate correct to the nearest whole number:

a. the distance between A and Bb. the time the plane takes to read point B c . the latitude of C (Take R = 6400km and π= 22/7)

#### Reading Assignment

New General Mathematics Chapter 7 pg 58-61,

Essential Mathematics for SS3, by AJS Oluwasanmi chapter 8 pgs 104-107

#### General Evaluation

- Find the distance between Bida (90N, 60E) and Addis Ababa (90N, 38.80E) measured along the parallel of latitude.
- Two places P and Q with longitudes of 1520E and 1710W both lie on the Equator.Find the shortest distance between P and Q on the Earth s surface.

- Two places P and Q have the same longitude. Their latitudes are 150N and 360S.Calculate the great circle distance between PQ.
- Two places X and Y on the equator are on longitude 670E and 1230E respectively. (a)What is the distance between them along the equator.

(b)How far is X from the North pole?(Take π = 22/7 and the radius of the earth as 6400km)

#### Reading Assignment:

NGM Chapter 7 pg 53-57

Essential Mathematics by AS. Oluwasanmi

#### Weekend Assignment

- The radius of Great Circles is approximately ……(a) 6500km (b) 6400km (c) 6500m (d) 6400m
- The circumference of a great circle with a radius of 6400km is approximately ……(a) 6200km (b) 6400km (c) 6300km 9d) 6100km
- P (440N, 100E) and Q (360S, 100E), what is the angular difference between point P and Q on the Earth’s surface?(a) 8o (b) 80o (c ) 70o (d) 20o
- What is the radius of parallel of latitude 300N?(a) 5530Km (b) 5540Km (c) 5440m (d) 5340Km
- What is the circumference of latitude 30o N ? (a) 34800km (b) 34900km (c) 35800km (d) 34700km

#### THEORY

- Alakuko and Meiran lie on the equator on longitude 70E and 900W respectively, if the circumference of the earth is 4000km find their distance apart to 3s.f.

- The position of A is 38oN, 73oE and the position of B is 38oN, 107oE. Calculate the distance from A to B
- along the parallel of latitude (b ) along the great circle.